Professional Development and Knowledge of Mathematics Teachers

Mathematics teaching and mathematics teacher professional developmentResearch on mathematics teaching and classroom situationsResearch on teacher and teacher educator knowledgeResearch on mathematics teacher education and professional developmentMediating mathematics in instruction: trajectories towards generality in “traditional” teachingIntroductionGeneralityIntroducing the frameworksThe MPM frameworkThe MDI frameworkGenerality as a goal in MPM and MDIGenerality in the MPMGenerality in the MDITheoretical/methodological overlaps and contrasts relating to generalityConcluding commentsNoteReferencesThe role of teachers’ knowledge in the use of learning opportunities triggered by mathematical connectionsIntroductionLength measurement teaching and learningConnectionsTeachers' knowledgeMethods and contextAnalysis and discussionFinal remarksAcknowledgementReferencesLearning to teach to reason: reasoning and proving in mathematics teacher educationIntroductionReasoning and proving in mathematics education scholarshipProblems with R&P and suggestions for how to address themStudies of practising teachersFramework and rationale of RaPiTEThe pilot studyOrganization and methodsResultsDiscussion and conclusionsReferencesThe role of frameworks in researching knowledge and practices of mathematics teachers and teacher educatorsIntroductionRationale and scope of this chapterWhat is a framework?Developing frameworks for the MTE level: a brief overviewA double-level use of frameworksAdapting frameworks from the classroom level to the PD levelFrom lenses to meta-lenses: a case of adapting a framework from the teacher level to the facilitator levelConcluding wordsNotesReferencesParallel stories: teachers and researchers searching for mathematics teachers’ specialized knowledgeIntroductionThe search for key factorsWhat knowledge do teachers talk about?Enrique's MTSKApplications of specialized knowledgeFinal observationsAcknowledgementReferencesThe specialized knowledge and beliefs of two university lecturers in linear algebraIntroductionTheoretical frameworkMathematics teachers' knowledgeThe mathematics teacher's specialized knowledgeTeacher beliefs about teaching and learning mathematicsMethodologyThe casesData collectionData analysisThe lecturers' knowledge and beliefsJordyCarlosDiscussion and conclusionsReferencesUsing the discourses of learning in education mapping to analyse research into mathematics teacher education and professional developmentIntroductionBackgroundVariation among discourses on learning in educationFirst example case: Variation TheoryCitations and referencesContextual factorsTheory of learning and/or theory of teachingSecond example case: Professional Learning Community (PLC) and collaborative learningCitations and referencesContextual factorsTheory of learning and/or theory of teachingDiscussion and conclusionsReferencesPromoting and investigating teachers’ professionalization processes towards noticing and fostering students’ potentials: a case of content-specific Design Research for teachersAdopting Design Research for teachersDesign Research as an established research methodology with big varietyAdopting Design Research for many teachers, not only with someContent-specificity and focus on teachers' professionalization processesFour intertwined working areas for PD Design ResearchThe case of DoMath, a PD Design Research project on noticing students' potentialsGoals, structure and background of the DoMath PD programmeProject design in three iterative cycles with mini cyclesExemplary design and research results in the DoMath projectDesign ResultsExemplary research results: extending the landscape of diagnostic perspectives and their relation to fosteringSummarizing and combining the design and research resultsZooming out: discussing the research approach Design ResearchFunding informationReferencesTheory-based design of professional development for upper secondary teachers – focusing on the content-specific use of digital toolsIntroduction and overviewProfessional development in mathematics education in Germany and the DZLM approachGeneral situation of PD coursesThe DZLM approachContext of the two PD coursesCommon design aspects related to digital toolsDesign Principles and accompanying research - realized in the PD course "graphic calculators compact"Design principles as realized in the course "graphic calculators compact"Competence-orientationParticipant-orientationStimulation of cooperationCase-relatednessVarious instruction formatsDomains of knowledge for teachers - design and evaluation of the PD course on "probability and statistics at upper secondary level"Context and overall design of the courseCollaborative design of the PD course - cooperation between DZLM team and regional facilitatorsAn example from the module "connecting data and chance"Addressed facets of teachers' knowledge and beliefsResearch on teachers' knowledge before and after the courseAcknowledgementReferences
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